An
extensometer used to
measure mechanical strain.
Strain gauges are often made from a very
thin wire looped back and forth to form many
parallel rows. This small package (about 2-5
mm on a side) , shown below, is then
bonded to a
surface along the axis of interest.
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Ig
In this case, the axis of measurement is vertical, since the loops are formed in that direction. The wire has a certain small resistance at rest, and this is measured by applying a small voltage (Vg) and observing the resulting gauge current (Ig). When a load (either tensile or compressionary) is applied to the member (and hence the gauge, if it's properly bonded to the surface of the member), the wire stretches (or contracts) in length. The multiple loops serve to increase the perceived wire elongation. Since the total resistance of a wire is proportional to its length (see this link for details), the change in the wire's length can be measured. Since strain is the ratio of the change in length to the wire's original (unloaded) length, you can compute strain from the change in length of one of the loops.
The small changes in resistance the strain gauge undergoes when it is loaded can be observed with a Wheatstone bridge circuit and an amplifier. This technique is used for many, many applications, such as industrial scales.